Pursuit Problem (Relative Velocity)

The relative velocity of the car with respect to the police, $v_{rel}$, is the velocity of the car, $v_{car}$, minus the velocity of the police car, $v_{police}$.

$v_{rel} = v_{car} - v_{police}$

The problem asks for the initial relative velocity at the moment the car passed the police. At this instant, the car is moving at its constant velocity, $v_{car}$. The police car is at rest, so its initial velocity is $v_{police,i} = 0 \text{ m/s}$.

Substituting these initial values into the relative velocity equation gives:

$v_{rel, i} = v_{car} - v_{police, i} = v_{car} - 0 = v_{car}$

$v_{rel, i} = 27 \text{ m/s}$